63663 ÷ 4 = 15915 R3
Alright, let's work through the division of 63663 by 4 step by step.

Step 1:
4 goes into 6 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1
Subtract 4 from 6 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 4

Step 2:
4 goes into 23 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 15
Subtract 20 from 23 to get 3.
Bring next digit (6) of the dividend behind the 3 and repeat the process: 36 / 4

Step 3:
4 goes into 36 9 times with a remainder of 0.
Write down 9 as next digit of of the result. 
Result so far: 159
Subtract 36 from 36 to get 0.
Bring next digit (6) of the dividend behind the 0 and repeat the process: 6 / 4

Step 4:
4 goes into 6 1 times with a remainder of 2.
Write down 1 as next digit of of the result. 
Result so far: 1591
Subtract 4 from 6 to get 2.
Bring next digit (3) of the dividend behind the 2 and repeat the process: 23 / 4

Step 5:
4 goes into 23 5 times with a remainder of 3.
Write down 5 as next digit of of the result. 
Result so far: 15915
Subtract 20 from 23 to get 3.

The final result is 15915 with a remainder of 3.